Dzhaliuk Nataliia Semenivna

Education: Drohobych Ivan Franko State Pedagogical University (specialty mathematics and computer sciences, 2001),

Postgraduate of Pidstryhach Institute for APMM NAS of Ukraine (01.01.06 algebra and number theory, 2009)

Scientific degree: Ph.D. Degree (01.01.06 algebra and number theory, 2010) ( thesis: "Factorization of matrices over polynomial and similar to them rings")

Scientific title: Docent

Position: Research Fellow (since 2012)

In Institute: from 2001

Research interests: linear algebra, matrix theory, matrix equations, matrices over commutative rings.

Major publications:

1.         The structure of solutions of the matrix linear unilateral polynomial equation with two variables (with Petrychkovych V.M.). Carpathian Math. Publ. 2017. 9, No. 1. 10 p.

2.         Absolute factorization of matrices in the rings of block-triangular matrices (with Petrychkovych V.M.). Applied problems of mechanics and mathematics. 11, 36 40, (2013). (in Ukrainian)

3.         The matrix linear unilateral and bilateral equations with two variables over commutative rings. (with Petrychkovych V.M.). ISRN Algebra, Volume 2012, Article ID 205478, 14 pages, doi: 10.5402/2012/205478.

4.         Semiscalar equivalence of polynomial matrices and tne solutions of the Sylvester matrix polynomial equations. (with Petrychkovych V.M.). Mathematical bulletin of the Shevchenko scientific society. 9, 8188, (2012). (in Ukrainian)

5.         Solutions of matrix polynomial Diophantine equation (with Petrychkovych V.M.). Applied problems of mechanics and mathematics. 10, 55 61, (2012). (in Ukrainian)

6.         The block diagonal parallel factorizations of matrices over principal ideal domains. Journal of National University "Lvivska Politechnika" Physical & mathematical sciences. 740, 5 10, (2012). (in Ukrainian)

7.         The matrix Diophantine equations AX+ BY= C (with Petrychkovych V.M.). Carpathian Mathematical Publications. 3 (2), 4956, (2011). (in Ukrainian)

8.     The association of factorizations of block triangular matrices and of their diagonal blocks over commutative principal ideal domains. Applied problems of mechanics and mathematics. 9, 82 86, (2011). (in Ukrainian)

9.     Parallel factorizations of matrices over rings and their connections (with Petrychkovych V.M.). Applied problems of mechanics and mathematics. 8, 7  17, (2010). (in Ukrainian)

10.  The uniqueness of the cell-triangular factorizations of the matrices over a principal ideal rings. Reports of the Academy of Sciences of Ukraine. 1, 7  12, (2010). (in Ukrainian)

11.  Description of parallel factorizations of polynomial matrices. Scientific bulletin of Uzhorod university. Series Mathematics and Informatics. 19, 31 37, (2009). (in Ukrainian)

12.  Common divisors of the block-triangular matrices over principal ideal domains. Applied problems of mechanics and mathematics. 7, 86 90, (2009). (in Ukrainian)

13.  Factorization of block diagonal and block triangular matrices over principal ideal rings (with Petrychkovych V.M.). Mathematical bulletin of the Shevchenko scientific society. 4, 7989, (2007). (in Ukrainian)

14.  On solution of matrix polynomial equations and on similarity of matrices (with Petrychkovych V.M.). Mat. Metody Fiz.-Mekh. Polya.  48, ( 4), 14  19, (2005). (in Ukrainian)

15.  On common monic divisors of polynomial matrices with given canonical diagonal form (with Petrychkovych V.M.). Mat. Metody Fiz.-Mekh. Polya .  45,  ( 3), 7 13, (2002). (in Ukrainian)

List of Conference Proceedings:

  1. Petrychkovych Vasyl', Dzhaliuk Nataliia Factorizations in the matrix ring and its subrings of the block matrices // The Fourth Conference of Mathematical Society of the Republic of Moldova: dedicated to the centenary of Vladimir Andrunachievici (1917-1997): Proceedings CMSM 4, June 28 July 2, 2017 Chisinau / ed.: Mitrofan Choban [et al.]. Chisinau: Institute of Mathematics and Computer science, 2017 (CEP USM). P.143146.
  2. Petrychkovych V.M., Dzhaliuk N.S. A bound on degrees of solutions of the matrix linear bilateral polynomial equation // Book of abstracts of the XI International Algebraic Conference in Ukraine dedicated to the 75th anniversary of V.V.Kirichenko (July, 2017, Kyiv, Ukraine). P.99.
  3. Petrychkovych V.M., Dzhaliuk N.S. Structure of solutions of the matrix Diofantine polynomial equations // International Algebraic Conference dedicated to 100th anniversary of L.A. Kaluzhnin. Book of Abstracts. Jule 712, 2014. Kyiv. P. 29.
  4. Dzhaliuk N., Petrychkovych V. Factorizations in rings of block diagonal matrices // International Conference Modern Problems of Mechanics and Mathematics. Lviv, Ukraine May 2125, 2013., Lviv. Abstract. Lviv: YA. S. Pidstryhach Institute for APMM NAS of Ukraine. V. 3. P. 181-183. (in Ukrainian)
  5. Dzhaliuk N., Petrychkovych V. Semiscalar equivalence of polynomial matrices and solutions of the matrix linear polynomial equations // 9-th International algebraic conference in Ukraine, L'viv, July 8-13, 2013: Book of abstracts. L'viv, 2013. P. 57.
  6. Dzhaliuk N., Petrychkovych V. Factorizations of block triangular matrices and their number // International Conference dedicated to the 120th anniversary of Stefan Banach, Lviv, Ukraine, 1721 September 2012. Abstracts of Reports. P. 268.
  7. Vasyl` Petrychkovych, Nataliia Dzhaliuk The matrix Diophantine polynomial equations // International Conference on Algebra dedicated to 100th anniversary of S.M. Chernikov, August 20-26, 2012, Dragomanov National Pedagogical University, Kiev, Ukraine: Book of abstracts. Kiev: Institute of Mathematics of UNAS, 2012. P. 116.
  8. Dzhaliuk N., Petrychkovych V. On the minimal degree solutions of the Sylvester matrix polynomial equations // International mathematical conference: abstracts of talks. Mykolayiv: Published by Mykolayiv V.O. Suchomlinsky National University, 2012. P. 138.
  9. Dzhaliuk N. S. The block diagonal parallel factorizations of matrices over principal ideal domains // Conference materials of young Scientists Pidstryhach reading 2012. Lviv, Ukraine, May 2325, 2012. P 3235. Lviv. [Electronic resource]. Access mode: http://www.iapmm.lviv.ua/chyt2012/materials/12.pdf (in Ukrainian)
  10. Dzhaliuk N.S., Petrychkovych V.M. The uniqueness of block diagonal parallel factorizations of matrices // 10-th Open scientific conference IMFS: [PSC-IMFS-10], (Lviv, Ukraine, May 1718, 2012.) / Lviv Polytechnic National University. Lviv: Lviv Polytechnic Publishing House, 2012. P. A32 [Electronic resource]. Access mode: http://psc-imfs.conference.lviv.ua/messages/psc-imfs-10-proceedings_175x250.pdf (in Ukrainian)
  11. Dzhaliuk N.S., Petrychkovych V.M. Block triangular matrices with absolute divisors separation // XIV International Scientific Kravchuk mathematical conference. Kyiv, Ukraine , April 19-21, 2012: .: Conference materials. P. 87. (in Ukrainian)
  12. Dzhalyuk N. S. The association of factorizations of block-triangular matrices // IV Conference of young Scientists Pidstryhach with Modern Problems of Mechanics and Mathematics. Lviv, Ukraine, May 2427, 2011. Abstract. Lviv: YA. S. Pidstryhach Institute for APMM NAS of Ukraine. P. 241-242. (in Ukrainian)

13.  Petrychkovych V. M., Dzhaliuk N. S. Factorizations in rings of block triangular matrices // 8th International Algebraic Conference in Ukraine . Lugansk, Ukraine, July 5 12, 2011, Book of abstracts . Lugansk Taras Shevchenko National University, Ukraine P. 159.

  1. Petrychkovych V.M., Dzhaliuk N.S. Matrix Diophantine equations // International Skorobohatko mathematical conference. Drohobych, Ukraine, September 1923, 2011. Abstracts P. 161. (in Ukrainian)
  2. Petrychkovych V.M., Dzhaliuk N.S. The uniqueness of solutions of matrix linear unilateral polynomial equations with two variables // All-Ukrainian Scientific Conference "Application of Mathematical Methods in Science and Technology", November 25-26, 2011. Abstracts. Lutsk, 2011. P. 7072. (in Ukrainian)
  3. Dzhalyuk N. S. Equivalence and factorizations of partitioned matrices // 7th International Algebraic Conference in Ukraine, 18 23 August, 2009: Abstract of talks. Kharkov, 2009. . 49.
  4. Dzhalyuk N. S. The divisors of polynomial matrices with parallel condition // Conference of young Scientists Pidstryhach with Modern Problems of Mechanics and Mathematics. Lviv, Ukraine, May 2527, 2009, P. 168 170. (in Ukrainian)
  5. Dzhalyuk N. S. On the factorizations of block triangular matrices and their uniqueness // XII international Scientific Kravchuk mathematical conference. Kyiv, Ukraine , May 15-17, 2008: Conference materials. .: TOV Zadruha" 600 p. P. 600. (in Ukrainian)
  6. Nataliia Dzhalyuk, Vasyl Petrychkovych On common divisors of cell-triangular matrices // International Conference Modern Problems of Mechanics and Mathematics devoted to the 80th anniversary of the birth of academician Pidstryhach Ya. S. and the 30th anniversary IAPMM he founded. Lviv, Ukraine May 2529, 2008, Lviv. Abstract. Lviv: YA. S. Pidstryhach Institute for APMM NAS of Ukraine. V. 3. P. 184 185. (in Ukrainian)
  7. Nataliia Dzhalyuk, Vasyl Petrychkovych The factorizations of block triangular integer matrices // International Skorobohatko mathematical conference. Drohobych, Ukraine, September 2428, 2007. Abstracts P.  88. (in Ukrainian)
  8. Nataliya Dzhalyuk, Vasyl Petrychkovych Factorizations of partitioned matrices and solutions of linear matrix equations // 6th International Algebraic Conference in Ukraine, 1 7 July, 2007: Abstracts of talks. Kamyanets-Podilsky, 2007. P. 75 76.

Phone service: (032) 258 96 22

E-mail: nataliya.dzhalyuk@gmail.com